2. WHAT ARE THE PARAMETRIC TESTS?
The parametric tests are tests applied to
data that are normally distributed, the
levels of measurement of which are
expressed in interval and ratio.
3. The Parametric Tests are:
t-test for Independent Samples
t-test for Correlated Sample
z-test for One Sample Group
z-test for Two Sample Means
F-test (ANOVA)
r (Pearson Product Moment Coefficient of
Correlation)
y = a +bx (Simple Linear Regression Analysis)
y = b0 + b1x 1 + b2x 2 + … + bnx n
(Multiple Regression Analysis)
4. WHEN DO WE USE PARAMETRIC TESTS?
the distribution is normal, that is when
skewness is equal to zero and kurtosis
equals 0.265.
the level of measurement to be analyzed
are expressed in interval and ratio data.
5. WHY DO WE USE PARAMETRIC TESTS?
They are more powerful compared to the
nonparametric tests.
HOW DO WE USE PARAMETRIC TESTS?
First, determine whether the data are
distributed normally or abnormally by
solving for the value of skewness and
kurtosis using the formula:
7. HOW DO WE USE PARAMETRIC TESTS?
Second, if the result of the skewness is
equal to zero and the kurtosis equals
0.265 then the distribution is normal.
Third, determine if the data are expressed
in interval and ratio data.
Fourth, use the parametric tests
8. WHAT IS INTERVAL DATA?
Interval data provide numbers that reflect
differences among items. With interval
scales the measurement units are equal.
Examples are scores of intelligence tests,
and time as reckoned from the calendar. They
have no true zero value.
9. WHAT IS RATIO DATA?
The ratio data are the highest type of scale.
The basic difference between the interval
and the ratio scale is that the interval scale
has no true zero value while the ratio scale
has an absolute zero value.
Common ratio scales are measures of
length, width, capacity loudness and others.
10. t – tests for independent samples
What is the t-test for independent
samples?
The t-test is a test of difference between
two independent groups. The means are
compared x1 against x2.
11. When do we use the t-test for independent samples?
When we compare the means of two
independent groups.
When the data are normally distributed,
Sk = 0 and Ku = 0.265.
When data are expressed in interval and ratio.
When the sample is less than 30.
12. Why do we use the t-test for independent
sample?
Because it is a more powerful test
compared with other tests of
difference of two independent
groups.
13. How do we use the t-test for independent
samples?
Use the formula: t =
𝒙𝟏 −𝒙𝟐
(
𝑺𝑺𝟏
+ 𝑺𝑺𝟐
𝒏𝟏
+ 𝒏𝟐
−𝟐
)(
𝟏
𝒏𝟏
+
𝟏
𝒏𝟐
)
where: t = the t-test
𝒙𝟏 = the mean of group 1
𝒙𝟐 = the mean of group 2
𝑺𝑺𝟏 = the sum of squares of group 1
𝑺𝑺𝟐 = the sum of squares of group 2
𝒏𝟏 = the number of observations in group 1
𝒏𝟐 = the number of observations in group 2
14. How do you solve t-test for independent samples?
Compute the sum of group 1 (Σ𝒙𝟏 ) and group
2 (Σ 𝒙𝟐 )
Determine the number of the observations in
group 1, (𝒏𝟏)and group 2, (𝒏𝟐).
Compute the sum of the squares of group 1,
(Σ𝑥1
2
)and sum of the squares of group 2, (
Σ𝑥2
2
).
15. Compute the means of group 1 and group 2.
𝒙𝟏 =
Σ𝒙𝟏
𝒏𝟏
the mean of group 1.
𝒙𝟐 =
Σ𝒙𝟐
𝒏𝟐
the mean of group 2.
Compute the 𝑺𝑺𝟏of group 1 and 𝑺𝑺𝟐 of group 2.
𝑺𝑺𝟏 = Σ𝑥1
2
-
(Σ𝒙𝟏
)2
𝒏𝟏
sum of squares of group 1.
𝑺𝑺𝟐 = Σ𝑥2
2
-
(Σ𝒙𝟐
)2
𝒏𝟐
sum of squares of group 2.
16.
17. Time in seconds it took the
rats to fall asleep. Example 1. Two groups of
experimental rats were injected
with a tranquilizer at 1.0 mg. and
1.5 mg. dose respectively. The
time given in seconds that took
them to fall asleep is hereby given.
Use the t-test for independent
samples at α =.01.Test the null
hypothesis that the difference in
dosage has no effect on the length
of time it took them to fall asleep.
1.0 mg dose 1.5 mg dose
9.8 12.0
13.2 7.4
11.2 9.8
9.5 11.5
13.0 13.0
12.1 12.5
9.8 9.8
12.3 10.5
7.9 13.5
10.2
9.7
18. Solving by the Stepwise:
Step 1. Problem: Is there a significant difference brought
about by the dosages on the length of time it took for the rats
to fall asleep?
Step 2. Hypotheses:
H0: There is no significant difference brought about
by the dosages on the length of time it look
for the rats to fall asleep.
H1: There is a significant difference brought about
by the dosages on the length of time it took
for the rats to fall asleep.
19. Step 3. Test Statistics
t –test for independent
samples
Level of Significance:
α = 0.01
df = 𝒏𝟏 + 𝒏𝟐 – 2
= 11 + 9 – 2
= 18
t .01 = -2.88 tabular
value at 0.01
21. Step 5: Decision. Since the t-computed value of -
.40 is not within the critical value of -2.88 at 0.01
level of significance with 18 degrees of freedom,
the null hypothesis is confirmed.
Step 6: Conclusion. This means that no significant
difference was brought about by the dosages on
the length of time it took for the rats to fall
asleep. Hence, the difference in dosage has no
effect on the length of time it took them to fall
asleep.
22. Example 2. The following are the scores in spelling of 10
male and 10 female AB students. Formulate the
hypothesis
Use the t-test at 0.05 level of significance.
Let this be your practice exercise.
Make sure that you will try this
before our meeting on Saturday.
Male (𝒙𝟏) Female (𝒙𝟐)
14 12
18 9
17 11
16 5
4 10
14 3
12 7
10 2
9 6
17 13
